2008/10/01 by Peter Hall, Soumendra N. Lahiri · 1 citation
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #math.ST #msc:62C20 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/07-aos534
published as Annals of Statistics 2008, Vol. 36, No. 5, 2110-2134 · Published in at http://dx.doi.org/10.1214/07-AOS534 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/10/01 · arxiv created 2008/10/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample, since we do not have a sample from the target. These and other considerations motivate the development of estimators of distributions, and of related quantities such as moments and quantiles, in errors-in-variables settings. We show that such estimators have curious and unexpected properties. For example, if the distributions of the variable of interest, W, say, and of the observation error are both centered at zero, then the rate of convergence of an estimator of the distribution function of W can be slower at the origin than away from the origin. This is an intrinsic characteristic of the problem, not a quirk of particular estimators; the property holds true for optimal estimators.